The Exciting Universe Of Music Theory

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Scale 111

Scale 111, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).


Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,3,5,6}
Forte Number6-Z3
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3777
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,2,6}
<2> = {2,3,7}
<3> = {3,4,8,9}
<4> = {5,9,10}
<5> = {6,10,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.433
Myhill Propertyno
Ridge Tonesnone

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Diminished Triads{0,3,6}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 111 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2103
Scale 2103, Ian Ring Music Theory
3rd mode:
Scale 3099
Scale 3099, Ian Ring Music Theory
4th mode:
Scale 3597
Scale 3597, Ian Ring Music Theory
5th mode:
Scale 1923
Scale 1923, Ian Ring Music Theory
6th mode:
Scale 3009
Scale 3009, Ian Ring Music Theory


This is the prime form of this scale.


The hexatonic modal family [111, 2103, 3099, 3597, 1923, 3009] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)


The inverse of a scale is a reflection using the root as its axis. The inverse of 111 is 3777

Scale 3777Scale 3777, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 111 is chiral, and its enantiomorph is scale 3777

Scale 3777Scale 3777, Ian Ring Music Theory


T0 111  T0I 3777
T1 222  T1I 3459
T2 444  T2I 2823
T3 888  T3I 1551
T4 1776  T4I 3102
T5 3552  T5I 2109
T6 3009  T6I 123
T7 1923  T7I 246
T8 3846  T8I 492
T9 3597  T9I 984
T10 3099  T10I 1968
T11 2103  T11I 3936

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 109Scale 109, Ian Ring Music Theory
Scale 107Scale 107, Ian Ring Music Theory
Scale 103Scale 103, Ian Ring Music Theory
Scale 119Scale 119, Ian Ring Music Theory
Scale 127Scale 127, Ian Ring Music Theory
Scale 79Scale 79, Ian Ring Music Theory
Scale 95Scale 95, Ian Ring Music Theory
Scale 47Scale 47, Ian Ring Music Theory
Scale 175Scale 175, Ian Ring Music Theory
Scale 239Scale 239, Ian Ring Music Theory
Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 1135Scale 1135: Katolian, Ian Ring Music TheoryKatolian
Scale 2159Scale 2159, Ian Ring Music Theory

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler ( used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.